lower bound: | 65 |
upper bound: | 68 |
Construction of a linear code [108,8,65] over GF(3): [1]: [109, 8, 66] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 2, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 1, 2, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2, 1, 0, 0, 0, 2, 0, 2, 2, 1, 0, 1 ] [ 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 2, 1, 2, 2, 1, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 2, 1, 1, 2, 2, 1, 0, 0, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 2, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1 ] [ 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 1, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 2, 2, 1, 1, 2, 1, 0, 1 ] [ 0, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 2, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 0, 2, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 1, 2, 2, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 2, 1, 1, 1, 0, 2, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 2, 2, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 1, 2, 2, 0, 1, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 0, 0, 1, 2, 0, 0, 1, 2, 2, 0, 0, 1, 1, 0, 2, 0, 1, 2, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 1, 1, 2, 0, 2, 0, 2, 1, 1, 2, 1, 1, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 0, 1, 2, 1, 0, 0, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 2, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 2, 1, 2, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 0, 2, 1, 2, 0, 1, 0, 0, 1, 2, 2, 1, 2, 1, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 1, 2, 0, 0, 2, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 1, 0, 0, 0, 1, 1, 2, 1, 2, 0, 2, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 2, 0, 2, 0, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 0, 2, 1, 1, 2, 1, 0, 1, 2, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 1, 1, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0 ] [2]: [108, 8, 65] Linear Code over GF(3) Puncturing of [1] at { 109 } last modified: 2009-01-13
Lb(108,8) = 64 is found by truncation of: Lb(110,8) = 66 GO2 Ub(108,8) = 68 follows by a one-step Griesmer bound from: Ub(39,7) = 22 follows by a one-step Griesmer bound from: Ub(16,6) = 7 vE2
vE2: M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory 41 (1995) 800-805.
Notes
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